Frequency domain iterative tuning for active noise and vibration control

Abstract

In this thesis a new adaptive control method, called Iterative Tuning in the Frequency Domain (FD-IT), is proposed for Active Noise and Vibration Control (ANVC). This approach is a gradient based self-tuning method which completely relies on analysis of the frequency response of system dynamics and the spectrum of signals. The new method is based on a new gradient estimation theory in the frequency domain. In this theory the gradient of the output spectrum with respect to controller parameters is expressed with the frequency response of dynamics and the spectrum of signals. When the performance gradient with respect to controller parameters can be expressed as some function of the signals’ spectrum, it can be computed out completely in the frequency domain. Similar to audio compression, when the system’s signals contain few frequencies, the computation of performance gradient can be greatly simplified by making ”partial modelling” with respect to those frequencies. According to the proposed theory, the new iterative tuning method, i.e., FD-IT, is developed for ANVC problems with periodic disturbances. It can tune the feedback/feed-forward controllers simultaneously with one experiment per iteration except some extra experiments for initial tuning. It covers both Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) systems. Furthermore, it can be extended to nonlinear systems as well. Some issues about the implementation of the iterative method are discussed. Through the comparison with some other popular active control methods in ANVC, the advantages of the new method, including: the flexibility in selecting controllers, the simplicity in control structure, and the convenience in implementation, are emphasized. The effectiveness and robustness of the proposed iterative tuning method are tested through simulated SISO and MIMO Linear Time Invariant (LTI) systems. Two simulated nonlinearities are used to illustrate the usefulness of the methods in nonlinear system as well. To show the practicability, the linear and nonlinear FD-ITs are implemented in an air-duct system with a PC-DSP based agent-architecture. All the results illustrate that FD-IT is an easy and effective approach to solve ANVC problems with periodic disturbances.

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